You have to do it thoroughly so that the rafters sit flush on it.
Tying a porch roof into existing roof.
After that to make it flush with the roof of the existing house cut the two outer rafters.
In any case the structure.
First the 4x4 beams need to be cut to the size of the existing roof so the porch roof and the edge of the existing roof will be even when the job is complete.
Attach the horizontal beam by using a nail gun.
Make a cutting on one of the sides of the horizontal roof beam on an angle.
Tying in to an existing gable roof.
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That fascia should be cut off where it is inside of the porch addition.
Then mount new trusses on the new addition walls.
Butt the first new truss against the old one.
Now take the 4x4 beams and erect them to the perimeter outside the porch about four feet apart.
I would frame a wall up flush with the brick and then use siding to cover it from there on up.